The value of the following limit is ________. $$\lim_{x \to 0+} \frac{\sqrt{x}}{1 - e^{2\sqrt{x}}}$$

We need to evaluate the limit:

Let $y = \sqrt{x}$. As $x \to 0^+$, $y \to 0^+$.

Substituting $y$ into the limit gives:

This is an indeterminate form of type $\frac{0}{0}$. Applying L'Hôpital's Rule by differentiating the numerator and the denominator with respect to $y$:

Therefore:

Thus, the value of the limit is -0.5.